Applied Mathematical Sciences

By: Yuri Kuznetsov

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Hardcover | 29 June 2004 | Edition Number 3

At a Glance

Hardcover
660 Pages

Edition Type
Revised

Dimensions(cm)
23.39 x 15.6 x 3.51

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The years that have passed since the publication of the first edition of this book proved that the basic principles used to select and present the material made sense. The idea was to write a simple text that could serve as a seri- ous introduction to the subject. Of course, the meaning of "simplicity" varies from person to person and from country to country. The word "introduction" contains even more ambiguity. To start reading this book, only a moder- ate knowledge of linear algebra and calculus is required. Other preliminaries, qualified as "elementary" in modern mathematics, are explicitly formulated in the book. These include the Fredholm Alternative for linear systems and the multidimensional Implicit Function Theorem. Using these very limited tools, a framewo:k of notions, results, and methods is gradually built that allows one to read (and possibly write) scientific papers on bifurcations of nonlinear dynamical systems. Among other things, progress in the sciences means that mathematical results and methods that once were new become standard and routinely used by the research and development community. Hopefully, this edition of the book will contribute to this process. The book's structure has been kept intact. Most of the changes introduced reflect recent theoretical and software developments in which the author was involved. Important changes in the third edition can be summarized as follows. A new section devoted to the fold-flip bifurcation for maps has appeared in Chapter 9.

Industry Reviews

Review of earlier edition

"I know of no other book that so clearly explains the basic phenomena of bifurcation theory." Math Reviews "The book is a fine addition to the dynamical systems literature. It is good to see, in our modern rush to quick publication, that we, as a mathematical community, still have time to bring together, and in such a readable and considered form, the important results on our subject." Bulletin of the AMS

From the reviews of the third edition:

"In the third edition of this textbook, the material again has been slightly extended while the main structure of the book was kept. ... the clear structure of the book allows applied scientists to use it as a reference book. ... Kuznetsov's book on applied bifurcation theory is still very useful both as a textbook and as a reference work for researchers from the natural sciences, engineering or economics." (Joerg Haerterich, Zentralblatt MATH, Vol. 1082, 2006)

"This book deals with the theory ofdynamical systems relevant for applications. The material is presented in a systematic and very readable form. It covers recent developments in bifurcation theory, with special attention to efficient numerical implementations. The text aims at an audience of graduate and Ph.D. students in applied mathematics, and researchers in science and engineering, who use dynamical systems and bifurcation analysis as a tool. Each chapter contains useful examples and many illustrations." (Dirk Roose, Bulletin of the Belgian Mathematical Society, 2007)

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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Differential Calculus & Equations Engineering & Technology Technology in General Engineering in General Number Theory Applied Mathematics Nonlinear Science

Introduction to dynamical systems	p. 1
Topological equivalence, bifurcations, and structural stability of dynamical systems	p. 39
One-parameter bifurcations of equilibria in continuous-time dynamical systems	p. 77
One-parameter bifurcations of fixed points in discrete-time dynamical systems	p. 117
Bifurcations of equilibria and periodic orbits in n-dimensional dynamical systems	p. 157
Bifurcations of orbits homoclinic and heteroclinic to hyperbolic equilibria	p. 195
Other one-parameter bifurcations in continuous-time dynamical systems	p. 249
Two-parameter bifurcations of equilibria in continuous-time dynamical systems	p. 295
Two-parameter bifurcations of fixed points in discrete-time dynamical systems	p. 407
Numerical analysis of bifurcations	p. 505
Basic notions from algebra, analysis, and geometry	p. 587
Table of Contents provided by Blackwell. All Rights Reserved.

Applied Mathematical Sciences

At a Glance

New Edition

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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